Abstract.

Intelligent agents embedded in cultural processes demonstrate remarkable powers of creation, transformation, stability and regulation. As G.P. Murdock said in his 1971 Huxley Lecture, culture and social structure are not divine law within which individuals simply satisfy their assigned objectives and then die. Culture gives agents the power to hyper-adapt: not only can they achieve local minima and maxima, they modify or create the conditions for adaptation. Culture transcends material and behavioural contexts. Cultural solutions are instantiated in material and behavioural terms, but are based in large part on 'invented' symbolic constructions of the interaction space and its elements. Although the level of 'intelligence' required to enact culture is relatively high, agents that enact culture create conditions to which other, less intelligent, agents will also adapt. A little culture goes a long way. We will consider culture design criteria and how these can be represented in agent-based models and how culture-based solutions might contribute to our global management of knowledge.

1 Introduction

Human culture is a creative and transformative force. From the standpoint of the sciences, culture has emerged from being an exotic curiosity in the 1930s associated with South Seas islands, tropical Africa and Highland New Guinea to underlying practical workaday methods, first in economic development projects, then industrial settings and more recently in software systems design relating to human-computer interfaces and human factors design.

In the development of agent-based software design a 'natural' approach to organising agents is implementing concepts such as society within which to embed agents. However, culture, the system of activities and resources that support humans in their social organisation, is scantly considered in the computational agent literature outside anthropological, sociological and occasionally economic or business models. Where culture does arise in the literature, it is most likely to relate to agents that relate directly or on behalf of people as cultural agents. So while there is some relevant literature that demonstrates considerable potential for the inclusion of culture-related concepts in mathematical and computational modelling, this is the product of a very small group of researchers. Even among anthropologists formal work exploring how culture 'works' is undertaken by few and explicitly eschewed by a sizable minority.

As an anthropologist I have to consider these issues. Is culture, despite its tenure in anthropology, just too 'fuzzy'? Or is it perhaps suitable for describing actual human groups, but not really as a means for constructing artificial, purposeful, systems? At the same time, there is no doubt that the behaviour we associate with culture is responsible for the collective achievements of humans that have moved us from the technologies of stick, bone and stone a million years ago towards the technologies of nanoengineering and quantum level computing which will permit us to further radically modify our lives, the world, and some day perhaps the universe.

I will argue that culture is indeed represented, implicitly, within many agent-based systems. It appears in the form of solutions that are inspired by the cultural knowledge of the system designers, in the conception of how agent societies should operate, and by including some of the mechanisms of communication, peer reaction and defining values that we can associate with cultural systems. Making explicit representations of cultural systems will bring these 'hidden' design elements into view and as a formal part of the agent framework, making possible more powerful agent-based solutions.

Anthropologists have proposed a range of definitions for culture over the past century. The development of the 'culture concept' is illustrated in Figure 1. In The shift from exclusively behavioural criteria to the inclusion of ideational components represents both development in anthropological theory as well as the impact of cybernetics and systems theory. One of the primary distinctions between Sociology and Anthropology is that anthropologists generally conceptualise societies as groups composed of individuals who coordinate in a holistic distributed manner through elaborated social behaviour and shared patterns of values. Prior to WWII this often traded under the term "superorganic". Murdock [1] argued that culture was "superindividual ... beyond the sphere of psychology ... It is a matter of indifference to psychology that two persons, instead of one, possess a given habit. ╔ it is precisely this fact that becomes the starting point of the science of culture" [1](207). When the concept of a system became available in the 1940s [2], anthropologists were able to progress their framework considerably as they now had a language for describing the relationship between complex unseen systems of thought and the expression of these as behaviour. Behaviour could be conceptualised as an inscription of individuals interacting driven by complex systems of thought.

2 Culture-based systems

Culture as a systemic concept has rapidly become pervasive outside anthropology in many cognate social sciences and humanities subjects. Despite this anthropologists are generally unable to define precisely what is meant by culture, nor do those who do precisely define culture agree. One explanation for difficulty in definition is that culture is not defined by a single process or system, but is the conjunction of many aspects of human cognition and organization [3]. These would include processes or systems relating to communication, learning, adaptation, representation and transformation. In short, what anthropologists, and increasingly others, now refer to as culture is an emergent phenomena (or perhaps even an apparent category of phenomena) - the result of interaction of different systems which are, at least in part, orthogonal to each other [4].

This was not unanticipated. Fischer, Lyon and Read [5] note that:

G. P. Murdock, in ... "Anthropology's Mythology", argued that neither culture nor social structure can be reified to serve as an explanation. Rather these are our characterization of patterns of interactions between individuals, not the source of these interactions. ... Murdock was introducing a program ... focusing ... theory on diversity of individual experience and choice, not commonality and conformance. Fischer and Lyon [6] on Murdock [7].

Marvin Minsky, in The Society of Mind, commented, "What magical trick makes us intelligent? The trick is that there is no trick. The power of intelligence stems from our vast diversity, not from any single, perfect principle". [8](308). Of course Minsky is referring to a single mind. To represent the diverse principles underlying cultural systems we might conceptualize culture as "the community of minds".

As Murdock and Minsky argue, culture cannot be represented in terms of uniform static structures; culture is dynamically enacted and constituted differently by different culture-enacting agents, but with results that are comprehensible, if not acceptable, to other agents. It is critical that we understand how cultural systems become distributed within a population in such a way that most agents can agree on what is a part of a culture and what is idiosyncratic. To connect a diverse community of minds culture must be relational; different agents will behave differently based on their relationship to other agents. Culture is enacted differently by different cultural agents, each of which has an understanding of how the other agents operate under different projections with respect to different relationships.

Fischer [9] relates some of the context for how implicit and explicit theories of culture have changed in recent decades, in particular the tensions between those who see structure and pattern and those who deny these in favour of performance, improvisation and smorgasbord emergent culture. Fischer observes this tension is resolved if we recognize that not least of the outcomes of cultural processes is to recreate the conditions for cultural technologies of thought and objects to operate, symbolically and materially. From this Fischer develops the principle of 'powerful knowledge', knowledge that is deontic, enabling the management and exploitation of processes which emerge from interacting cultural agents and their knowledge.

Fischer and Read [10] outline an approach to focusing on culture in a way that the duality between ideation and behaviour could be represented in concrete models. The basic concept is simple; that we can represent culture as a collection of discrete symbolic systems, possibly not logically consistent with each other. These systems of symbols are shared between agents to varying degrees of detail and consistency. It is when agents instantiate these within a common interaction space into a set of behaviours that commonalities and inconsistencies are reconciled. Indeed, the patterns of behaviour that emerge that are recognised as culture may emerge from underlying symbolic systems that are apparently at odds with each other, both within the same agent and between agents.

3 Approaches to Computational Culture

The 2004 European Meetings for Cybernetics and System Research included sessions relating to cultural systems with contributions exploring the use of culture in mathematical and computational models. These were not new approaches in the sense that the researchers concerned have been working with and promoting these ideas for some time. They are finally beginning to have traction.

Reynolds and Peng [11] demonstrate how a simple model of culture can be instantiated in an agent population to adaptively solve 'real world' optimization problems. They outline a method based on the evolutionary Cultural Algorithms approach originated by Reynolds [12] that models an agent population using diverse symbolic knowledge to adaptively converge towards solutions to optimization problems. In this case they demonstrate that CA can be applied to solving problems in engineering design as a result of emergent features based on adaptive cultural systems with the ability to learn and adapt at a more abstract level than conventional genetic algorithms.

Reynolds and Peng situate culture within the evolutionary process by expanding an agent's phenotype to include acquired characteristics associated with knowledge-based solutions; an individual's fitness is now associated with both their hereditary fitness and their cultural fitness. The latter includes their individual ability to use cultural resources and the fitness bestowed on them by others within the cultural 'swarm' by others' modifying and expanding the knowledge and belief resources in the system adaptively over time. Thus individual fitness is not only about individual's transmitting their individual phenotypes across generations, but about transmitting their knowledge adaptations as well. Furthermore, individual fitness is directly linked to modifications that the individual agent and other agents introduce.

Using the three principles of cognitive relativity, rationality and clarity, Ezhkova [13] addresses culture by an examination of shared experience and how asymmetric but inter-adapted 'clarity' emerges from these shared experiences. Taking culture as a self-organizing complex phenomenon, she notes that as a result of cognitive relativity a culture can be examined from a number of different observer perspectives, where a culture is observed as a unitary 'actor', the community of individual actors who enact a culture, or indeed in a comparative sense as one of a set of cultural systems. Furthermore, these different perspectives can be nested by a single observer such that all are available simultaneously, producing a continuum of composite perspectives and potential actions to be taken.

Ezhkova argues that rationality is thus a relative condition: "Rationality rests on the particular nest of action in which one must exercise decision." Clarity is how Ezhkova denotes the ability to differentiate and classify the variety of inputs agents are exposed to; effectively underlying the ability to create categories. She outlines several approaches to measuring and implementing clarity. Ezhkova proposes the process of seeking clarity as a key cognitive navigational tool, the driver for adaptation in order to maximize success. Culture is a tool for recognition of key stable patterns, using clarity to situate culture in an evolutionary context: "the evolutionary meaning of clarity: what is clear survives". This is a very important point, particularly in a cultural context. Culture emerges, in large part, because of the distribution of a shared sense of clarity rather than specific shared bits of knowledge which tends to be distributed.

Ballonoff [14] presents a three level framework of measurements relating to a culture driven system, i) corresponding to material processes, ii) the impacts of cultural operators on i), and iii) measurements relating to the evolution of ii). That is, in an "ethnographic view", population and genetic statistics are the base phenomena (I), culture modifies these measures over time as events (II), and the pattern of change is governed by measurements of II (as per work of Ezhkova). With respect to a "real" system G related to some set of cultural systems C instantiation is "prediction or computation from the cultural system to create a particular instance of the real system". G evolves forward under evolutionary operators, and C under cultural evolutionary operators, and the effects of both these must occur on the same real systems in concert, clearly constraining each other. He concludes that these constraints can filter the huge lattice of possible relationships between G and C, making it possible to predict possible future cultural structures realizable in the real system.

Hunters and gatherers in Arctic societies undergo strong selection in an adaptationist paradigm. Read [15] uses one such society, the Netsilik, in his formal analysis of the role of resilience and robustness in increasing the adaptive capacity of human societies. Read uses Netsilik Inuit data as an extreme example of the cultural adaptations which allows individuals to modify environmental constraints; their adaptation to an Arctic environment exemplifies the way in which behaviour has both a material and an ideational/cultural dimension. Human societies, Read argues, have developed both resilient and robust responses to shocks in order to satisfy environmental imperatives and cope with culturally generated tensions. Using the basic subsistence challenges of living in inhospitable Arctic conditions along Hudson Bay, Canada, Read shows how relatively simple cultural solutions to real problems sometimes have longer term consequences which require some kind of resolution. The resolution to one problem, in turn, may lead to further dilemmas which then need some form of resolution.

Read stresses the importance of self-monitoring of a system as part of the system's resilience, particularly cultural systems with group level benefits due to difficulty maintaining a stable configurations of behaviour with respect to social and cultural relationships between individuals. Behaviours such as seasonal fishing and hunting are relatively stable while ideational behaviours are far less so, requiring repeated and frequent monitoring by individuals of their relationships with other individuals. "People do what is required to make a cultural model work in the real world" even if it means violating ordinary norms of behaviour. Individual instantiation of cultural models results in group-level behaviour that benefits those individuals.

Read presents a dynamic mathematical approach for studying "real world" systems with interacting material and ideational processes and an insightful explanation for specific cultural behaviours which, when taken in isolation, may seem difficult to fathom; when understood as part of a complex cultural system that provided the Netsilik Inuit with sufficiently robust responses to shocks to retain some continuity of collective notions of who and what the Netsilik were, with resilient responses that provided the flexibility to survive unstable situations.

Employing the deontic logic of permissions and obligations rather than the imperative logic of possibility and necessity, Fischer [9] argues that domain knowledge need not be true, it need only be enabling or effective - what he calls "powerful knowledge". Transforming information or experience into knowledge is a role associated with culture but people embedded in a culture have many ways of carrying out these transformations. An understanding of culture cannot be derived from treating an instantiation as if it were an underlying principle. Indeed, he suggests that when looking at the level of instantiation it is both plausible and sometimes likely that underlying principles will not be expressed in favour of contingent events.

Reynold's and Peng, Ezhkova, Ballonoff and Read advance our understanding of cultural systems of agents, demonstrating that models based on diverse symbolic knowledge in concert with a population that uses this knowledge can apply that knowledge in a dynamic manner to solve new material problems. They identify additional requirements for this knowledge: diverse knowledge domains that are distributed across the population. There are adaptive advantages to having a distributed and diverse knowledge environment both for the population as a whole and the individuals within it, even those that are themselves less adapted. These models demonstrate that even in a highly constrained environment with somewhat unforgiving evolutionary forces at work, cultural systems require more than one type and distribution of knowledge to learn and adapt.

4 Cultural Instantiation

Fischer and Read [10] initiates a programme to develop instantiation of an ideational system as a basis for formally describing relationships between ideational and material processes and increasing the efficacy of using more integrated models and agent-oriented simulations for understanding cultural processes in particular.

In the crudest terms an instantiation of an ideational system is the production of an instance of behaviour conditioned by an ideational system within a given material context, which may include other agents each instantiating the same or a different ideational systems of their own - the reduction of the possible to a presence. Instantiation is an interface between ideas and action, conception and creation, thinking and doing. Models embedding both material and ideational themes are important if we are to advance our understanding of human lives embedded in the world. Many of the problems anthropologists investigate relate to an ideational structure or process embedded within a material context (or vice versa).

Ideational systems considered in isolation are difficult to evaluate. Behavioural processes are difficult to interpret. By embedding material and ideational components within an integrated model, the properties of ideational systems, and observable indices of these, may be identified. In this way we can create models that both take account of how the physical context limits the application of ideational resources and how ideational resources influence the structure and recreation of important aspects of the physical context. This is important because considering ideational resources in the context of their application solves many of the philosophical problems that arise when considering the ideational or material issues alone (such as infinite regress, reflection, non-determinism, non-essentialism). Although there are a large number of ways for an ideational resource to be instantiated in a given material context, these will generally be far fewer than the number of ways in which it can be imagined to instantiate. Additionally, the same basic ideational resource can/will be instantiated differently in different contexts.

In modelling instantiation, we represent a group of people as a collection of individual agents, not an abstract aggregate. This makes it possible to study why and how patterns emerge, which cannot be done if we only consider the aggregate that exhibits the pattern. Instantiation is a process that mediates the mapping from ideational structures to physical effects. Behaviour is not a direct result of ideational systems, but of the 'rules' of instantiation of an ideational system. Cultural schema need not be directly linked to behaviour, nor need they be functionally dependent on 'what works', at least until a system of instantiation can no longer reliably connect cultural schema to material requirements - a condition that we posit is relatively infrequent. Thus cultural schema can be relatively stable and conservative while being adaptive to context and supporting relatively rapid adaptation by modifying the pattern of instantiation rather than the pattern of fundamental ideas and thought. Also, instantiation occurs whenever idea contacts the world. The result may stem more from the external context than from what was 'intended' or 'desired'. That is, cultural instantiation is a process of ideational principles of multi-agents interacting together, often within a material context. The result, whatever it is, is the instantiation. Agents rarely fulfil their goals in full, and sometimes not at all.

For example, Read [18] relates our use of instantiation in research on a universal cultural category, kinship terminologies. In the course of developing a computer program, Kinship Algebra Expert System (KAES) [19], to assist in the production of algebraic models of kinship terminology we made a number of important discoveries. Following Leaf [20], a kinship terminology can be represented entirely in terms of native thinker judgements of the relationships between terms without reference to external genealogical concepts [18].

KAES identifies an underlying algebraic structure for this representation of the terminology (if there is one... so far all complex terminologies we have tried are amenable). Based on graphical input relating to a given kinship terminology and knowledge about the relationships between terminologies (in terms of the terminology only) KAES produces results that can be instantiated in a given real or model population, based exclusively on internal properties of the kinship terms and indigenous judgements of lexical properties of the terms and very basic relationships between terms based on entirely internal criteria. Unlike most attempts at formal modelling our approach make no recourse to hypothetical external reference frameworks such as a genealogical grid.

This is not the first model to be based on lexical properties of kinship terms. The componential systems developed in the 1960s (cf. [21]) were based on lexical properties associated with kin terms, and were formal in a trivial sense. They did not result in structures which were general because the formal model used had no analytic capacity beyond establishing that the relationships in a given terminology were consistent. Fischer [22] implemented a general formal representation suitable for instantiation, but while formally based, the fundamental properties it depended on were assumed to be given. Other algebraic approaches to terminological analysis have be extant for 50 years, but have either fitted terminologies to prescribed structures, or been difficult to instantiate on actual populations... there was no easy way to relate the algebraic account and the instantiation of kin terms in groups of people. Additionally these systems tended to depend on considerable algebraic creativity and understanding on the part of the analyst.

Our model is algebraic and algorithmic. That is, the models are algebras, and producing these algebras is done following a algorithm. We have developed a computer program loosely based on Read and Behren's earlier KAES [23], but rather than an expert system which assists in making decisions towards creating an appropriate algebraic account, our program generates the algebras directly from the source data (lists of terms and indigenous judgements on relationships between terms), with only a single decision in the process whether to represent sex as a feature of individual terms, or whether to treat sex as a bifurcation whose associated productions are structurally equivalent. We have retained the KAES label for historical continuity.

Although doubtless a bit abstract for some, KAES is significant. Most important is the result that is emerging from using KAES: the strong suggestion that most, if not all, elementary and complex kinship terminologies can be described in terms of an algebraic structure. This is significant, because there are many more terminologies possible that do not possess such a structure. That the human mind should settle on the more limited set implies some deep commonalities in the forms of logic that humans employ. It is also significant because:

it is a formal model of an ideational system derived entirely from judgements on terminological relationships, not on an instantiation in a population.

will produce results that are predictive of the set of instantiated relationships in specific populations.

It is also significant because it is a good example of how the results of the analysis of an ideational system can be directly introduced into subsequent models without transformation or 'tailoring' for the purpose. That is, it provides a means of representing the potentialities of a cultural system and relating these to specific contexts without performing the reductions a particular context would normally require - reductions are properties of the process of instantiation.

One thing that almost all kinship terminological systems have in common is that they must be instantiable to be useful and to reproduce themselves. Being instantiable implies certain properties that an instantiable system must have to 'become present'. Among these is some extent of stability. Most systems can change relatively easily and remain a system. Although it is possible to modify an algebra and have a result that is an algebra, this is much 'harder' to do. Therefore systems that must be stable will benefit if they must also be logically equivalent to an algebra (this would not be unique to algebras but a property to any system of symbols with internally defined rules of production). Beyond this we found that the approach that Read used to identify the algebraic structures underlying terminologies itself could be improved and better understood by taking instantiation into account. That is, by taking into account the need to be instantiable and stable, the algorithm became simpler and more understandable, and this could be used as an evaluation metric for choosing one approach over another. The resulting algorithm from this approach was much more unified than Read's earlier attempts, suggested ways of dealing with terminological systems that had previously been resistant to explanation (classificatory terminologies) and the role of gender was significantly improved.

The most remarkable outcome, from our perspective at least, is that by combining a small subset of knowledge about the ideational properties of the terminology, the generating terms of the algebra, and a small subset of the knowledge about instantiation, how the generating terms are instantiated, that the structure of the complete terminology can be generated [19] precisely. To our knowledge this is the first example of a predictive model of a symbolic system that can be based entirely on data consisting of relational judgements of the relationships between tokens. This result is not possible by looking at the behavioural data alone, nor by construction of an ideational model alone, only by combining aspects of both in a single model.

In some ways this returns to the distinction between competence and performance proposed by Chomksy [24]. Perhaps this is where we often go wrong. We cannot simply analyse the structures that occur, because there are 'errors' and little variants that will 'spoil' any formal description. But this is not the real reason. We cannot analyse narrow behaviour because it is only a tiny fragment of what is going on, and a single behaviour can potentially impact many different ideational schemas, but is what results because of instantiation. That is, contrary to Chomsky's conjecture that separated the analysis of competence from that of performance, the point of instantiation between these is critical in analysis from either ideational or material perspective. Ideational analyses that ignore altogether issues of instantiation cannot account for either the variation or stability in culture, nor can materialist analyses that ignore the principles of instantiation of practice or behaviour.

5 Describing Cultural Processes using Deontic Logic

Most cultural systems cannot as easily be represented by 'pure' algebrae as kinship terminologies. However, our conjecture regarding cultural domains [9] only requires that a significant component of a cultural domain be logically equivalent to a model governed by an internally consistent set of principles.

The logics generally underlying models based on statistically derived aggregated variables and their interactions operates on the assumption of direct or indirect causality where probability is an integral property of variables. Either a variable causes effects on another variable (e.g. number of calories ingested and energetic capacity), or the variable's value is proportional to another (perhaps unknown) variable that causes (is responsible for) some of the variation in the second (e.g. age and grey hair). The result is a causal logic operating on probabilistic relationships. While this approach is tractable with small models, it does not scale up well to larger models, and often leads to confusion in interpreting the contingent results of the model - whether these are to be attributed to the model or to factors outside the model. The resulting models are not well suited to supporting multi-agent models.

We can enhance this logic by adding deontic principles in addition to causal principles. Deontic argumentation originally grew out of moral philosophy, with the first modern formulation as a logic by Mally ( [25]. See Lokhorst and Gobel [26] for a discussion of Mally's logic), who developed a logic based on propositions that assert that certain actions or states of affairs are morally obligatory, morally permissible, morally right or morally wrong - a logic of what ought to be given moral principles. There were serious problems with Mally's logic, but other deontic approaches have been developed (e.g. Endorsing [27], Maibaum [28]) with respect to obligations and permissions. Deontic logic can be applied both to ideational domains with respect to knowledge-based rules (Fischer and Finkelstein [29], Fischer [22]), as well as to material systems [28]. Deontic logic as I am using it follows Maibaum [28], which implements it by adding modal operators to a conventional predicate logic.

Deontic operations (obliged and permitted) are based on enablement and constraint as the basic principles for describing relationships, and can account for some apparent indeterminacy in a phenomena in terms of enabling and constraining the application of logical formulae (some f leading to actions or states). Weak determinism is denoted using the operator obliged ('do f when permitted'), stronger determinism by OBL ('do everything possible to do f') and constraints on statements by ~not permitted (~permitted) to prohibit a future instantiation of an action or result. The permitted operation is likewise indeterminant.- permitted does not require an action, it only allows (or enables) it at some future point. For example, if we have the following model of a process:

~permitted B -- constrain B \
Loop:generate A -- a generator of condition A \
if A then obliged B -- if condition A the proposition B iif B not constrained. \
if B then halt -- exit this segment \
generate C -- a generator of condition A \
if C then permitted B - enable B \
if B then halt -- exit this segment \
goto loop

Figure 2. A simple deontic model

Using deontic principles to interpret the statements, the model will execute Loop once, but halt at the second halt statement, since at the first conditional B is constrained, and cannot be expressed until the constraint is lifted. However, once B is permitted, B is expressed (if the first conditional is still valid) because it then obliged. In a variant formulations it is possible to use a weaker definition of oblige that applies only at the time of the conditional. In this case the model would execute Loop twice, and exit at the first halt statement on the second iteration. The first approach is representative of a parallel/declarative architecture. The second (weaker) is typically procedural.

The practical consequences of the deontic approach for modelling is that it provides tools for incrementally building models of processes, is adaptable to incorporation of agent-based description as well as aggregates, and more cleanly separates contingency accounted for within the model from contingency external to the model.

Fischer and Finkelstein [29] employed a deontic logic developed by Maibaum [28] called Modal Action Logic (MAL). Rules are expressed '(IN CONTEXT c) WHEN agent is performing action a THEN result'.

For example, ignoring some details of quantification, one observation derived from our case study of arranged marriages in Pakistan was:

in_public(girl) : [sing(girl,suggestive(lyrics))] -> character(girl, bad). \
(gloss: if the girl is singing suggestive lyrics in public then the girl has bad character)

In essence there is a governing proposition that is action related, defining a context frame for further conditions, which in turn contextualise the action. The use of this formulation solved a number of problems in representing processes because conditions and outcomes could be better organized in terms of the actions in the process. More important, it facilitates a formal representation of ethnographic data in a manner that is closer to the data as it is collected. Ethnographic data are not usually collected in the form of rules - rules are the result of analysis. Ethnographic data are more often in the form of sequences of declarative propositions. It is only after considerable observation and inquiry that the preconditions and results of these actions in specific contexts can be assessed. Thus we can further explore the action: sing(girl, suggestive(lyrics)) in:

at_mindhi_of(girl,bro):[sing_to(girl,family(bride))]-> \
permit(sing(girl,suggestive(lyrics))) \
(gloss: when a girl is attending the mindhi (pre-marriage eve) ceremony of her brother and the girl is singing about the brides' family then the girl is permitted to sing songs with suggestive lyrics).

This approach facilitates the incremental development of rules from propositions. Processes with many concurrent actions can be represented. There is independence between the logic and the possibly stochastic events the logic applies to. These features make this formulation ideal for multi-agent modelling.

We can quantitatively evaluate these models without resort to aggregation by using evaluating changes in entropy between the expanded ideational structure and the instantiated structures (see Fischer [31] following Gatlin [30]). Of course, applying information theory [32] to our analysis depends on our capacity at some point to at least enumerate states possible for a given variable (to determine maximum uncertainty), and ideally to identify probabilities (or statistical proxies) for each state to calculate the minimum uncertainty. Deontic logic has no direct capacity to process this information. So why is it relevant to using information theory as a means to assess the interrelationships between the variables used to monitor or describe a particular context?

Within a flow of independent (or external) stochastic events, a logical model employing the deontic operators obliged, ~obliged, permitted and ~permitted to actions/states can modulate the flow of logic in response to these events using much simpler models that than would be required if we were to insist on a local causal model incorporating both variable values and variable degrees of applicability.

Deontic logic thus provides tools for representing not only direct causality, but also to describe in greater detail the context or conditions under which a causal relationship operates. For example, in Figure 2. if we designate stochastic parameters for the generate statements for A and C, their correlation with B is co-dependent. Given a data set consistent with Figure 2. the outcome of this co-dependence as expression of B might be described using only conventional statistical methods (such as multiple or partial correlation). However, Figure 2. proposes that the intrinsic correlation between A and B should approach 1 in isolation, (and the correlation between A and C could be zero) but within the wider model this expression is mediated by C. C thus controls the expression of the relationship between A and B, and the relation between B and C can only be expressed (in Figure 2.) given A. The deontic framework for modelling allows us to express in greater detail how the different variables interact with each other than simpler structural logics such as typically underlay causal path analysis or other conventional quantitative analysis in use. But, importantly, deontic logic is consistent with these; it merely permits more mechanical detail in processes which have structural constraints.

A deontic model formulation requires finding/constructing absolute enabling conditions, which can have a complex underlying aetiology. In other words, we have to either have enough detail on the process under investigation to posit and test constraints, or we have to attempt to predict constraints from the 'holes' in the conventional structure. However, constructing deontic models can be done incrementally in its concurrent/declarative formulation which makes it convenient to implement as independent statements that 'communicate' based on changes by the statements to the global data set. Such models are typically easier to produce and interpret than models based on first order linear causal interactions. Indeed the use of a distributed deontic framework for situating data collection and analysis may prove to be a useful starting point for progressing more detailed quantitative approaches.